Nonlinear free and forced thermo-electro-aero-elastic vibration and dynamic response of piezoelectric functionally graded laminated composite shells, Part I: Theory and analytical solutions

Nonlinear vibration and dynamic response of simply supported piezoelectric functionally graded material (FGM) shells under combined electrical, thermal, mechanical and aerodynamic loading are studied in this paper. The material properties of the shell are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of the constituents. The third-order piston theory is employed to evaluate the aerodynamic pressure. The governing equations are derived using improved Donnell shell theory ignoring the shallowness of cylindrical shells and kinematic nonlinearity and the physical neutral surface concept are taken into consideration. The Galerkin method, Volmir's assumption and the multiple time scales perturbation methods are used for the nonlinear dynamical analysis of shells to give the expression of natural frequencies, the nonlinear dynamic responses and the primary resonance phenomena. The influences of the shell geometry and piezoelectric thickness, temperature change, external constant electric voltage and aerodynamic loads on the nonlinear dynamic behavior of the piezoelectric functionally graded shells through a comprehensive parametric study are discussed in details.